If you let it drag behind you, the ball and chain will slow your movement speed to a crawl and prevent you from climbing, swimming, or ascending with a jetpack. Attempting to fly using a jetpack with a ball and chain shackled to you will only allow you to hover at the maximum length of the chain, but the Cape will still slow your descent as usual.
Picking up the ball lets you move normally, but naturally this prevents you from holding anything else in your hands.
The ball can also be thrown at enemies, but it doesn't have much range; it is, after all, tethered to you.

Don't mess with Kali, it can ruin a perfect game

It's possible for the ball and chain to trap you in such a way that you can't escape, so be careful not to let the ball get into places it can't be unhooked from while traversing unusual terrain like that pictured on the right.

If the ball and chain is thrown into lava, or smashed by a crusher trap, it will be destroyed leaving you free of its effects. However, a new ball and chain will appear at the start of the next level.

In some cases, (such as custom levels created for this purpose) the ball and chain can actually come in handy by using it to get past some difficult areas such as lava. By placing the ball on a platform and walking below it, you will hang in mid air, still able to move horizontally below the platform. This is useful if the platform ends on the other side of the obstacle you are trying to get to, but can trap you if you're not careful.

Using the physics that prevent you from swimming up, you can easily kill Megamouth by swimming back and forth right over it. Then when Megamouth is dead, you can pick up the Ball and Chain and exit the water.

The ball and chain can also be used to reduce fall damage by falling off of the edge of the pit, and throwing the ball in a different direction than you, and using the difference in speed to slow you down when the ball reaches the end of the chain above you. This method is dangerous, and usually results in at least 1 point of fall damage, but in the hands of an expert, negative Favor with Kali can actually be a blessing using the ball and chain.

Spelunky's ball and chain is most likely a reference to Nethack, where a ball and chain can be received by reading a scroll of punishment or potentially by angering your god; it drags along behind you and hits you in the head when going down stairs, but can be picked up and used as a (very heavy) weapon, or thrown to drag you along with it. However, in Nethack there is a plethora of ways to remove the punishment.